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A039969 An example of a d-perfect sequence: a(n) = Catalan(n) mod 3. 8
1, 1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This is A006996 with all its terms repeated three times, except the initial term only twice. A006996 is a fixed point of the morphism 0 -> 000, 1 -> 120, 2 -> 210. [The original comment edited by Antti Karttunen, Aug 14 2017]

Equals Catalan(n) mod 3. (Cf. A000108.) - Paul D. Hanna, Jun 20 2003 [confirmed by Christian G. Bower, Jun 12 2005]

Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10000

D. Kohel, S. Ling and C. Xing, Explicit Sequence Expansions [Broken link?]

D. Kohel, S. Ling and C. Xing, Explicit Sequence Expansions, Sequences and their Applications, Discrete Mathematics and Theoretical Computer Science 1999, pp 308-317.

Index entries for sequences that are fixed points of mappings

FORMULA

a(3n) = A006996(n). - Antti Karttunen, Aug 14 2017

MATHEMATICA

Take[ Flatten[ Nest[ Flatten[ # /. {1 -> {1, 2, 0}, 2 -> {2, 1, 0}, 0 -> {0, 0, 0}}] &, {1}, 4] /. {1 -> {1, 1, 1}, 2 -> {2, 2, 2}, 0 -> {0, 0, 0}}], {2, 106}] (* or *)

Table[ Mod[ Binomial[ 2n, n]/(n + 1), 3], {n, 0, 104}] (* Robert G. Wilson v, Sep 09 2005 *)

Mod[CatalanNumber[Range[0, 110]], 3] (* Harvey P. Dale, Oct 23 2017 *)

PROG

(MAGMA) [Catalan(n) mod 3: n in [1..80]]; // Vincenzo Librandi, Jul 14 2015

(PARI) A039969(n) = ((binomial(2*n, n)/(n+1))%3); \\ Antti Karttunen, Aug 13 2017

CROSSREFS

Cf. A000108, A010872, A039972.

Cf. A006996 (trisection).

Sequence in context: A163326 A028953 A037865 * A039967 A258133 A123186

Adjacent sequences:  A039966 A039967 A039968 * A039970 A039971 A039972

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Christian G. Bower, Jun 12 2005

Offset corrected from 1 to 0 by Antti Karttunen, Aug 13 2017

STATUS

approved

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Last modified February 19 09:13 EST 2018. Contains 299330 sequences. (Running on oeis4.)